Phil’Em Up Poker

When I playing Mississippi Stud in Vegas last week, I overheard someone mention a game called Phil’Em Up Poker. I looked at the game, to see if collusion would yield an edge. The rules are pretty simple. The game is played with a 52-card deck plus a Joker which may be used for Aces, straights, and flushes. Each player bets an Ante, and receives two hole cards. Two community cards are dealt face up. Each player may either make an additional 1x bet (i.e., “double-up” his action), or check, before the 3rd community card is exposed. If a player makes a pair of Tens or better, he wins according to a paytable. There is no dealer hand. The house edge is a reasonable 3.3%.

Optimal Outcomes for Phil’Em Up Poker

Hand

Bet

Combinations

Probability

Payout

Return

FIVE_ACES

2

5

0.00000035

1000

0.000697

natural ROYAL_FLUSH

2

20

0.00000139

250

0.000697

wild ROYAL_FLUSH

2

100

0.00000697

100

0.001394

natural STRAIGHT_FLUSH

2

180

0.00001254

50

0.001254

wild STRAIGHT_FLUSH

2

720

0.00005018

25

0.002509

FOUR_OF_A_KIND

2

4,140

0.00028853

20

0.011541

FULL_HOUSE

2

21,840

0.00152212

15

0.045664

FLUSH

2

39,020

0.00271946

9

0.048950

STRAIGHT

2

77,460

0.00539850

7

0.075579

THREE_OF_A_KIND

2

211,200

0.01471939

3

0.088316

TWO_PAIRS

2

365,640

0.02548294

2

0.101932

High Pair

2

1,562,112

0.10886993

1

0.217740

Low Pair

2

75,648

0.00527222

-1

-0.010544

HIGH_CARD

2

339,708

0.02367563

-1

-0.047351

STRAIGHT

1

25,200

0.00175629

7

0.012294

THREE_OF_A_KIND

1

105,600

0.00735969

3

0.022079

TWO_PAIRS

1

327,360

0.02281505

2

0.045630

High Pair

1

922,608

0.06430030

1

0.064300

Low Pair

1

3,514,752

0.24495734

-1

-0.244957

HIGH_CARD

1

6,755,112

0.47079118

-1

-0.470791

total

14,348,425

-0.033067

expected

14,348,425

Collusion doesn’t help. That’s because only 3.8% of hands are bet on a draw only. Collusion will change few decisions, and result in little gain. With 7-player collusion, perfect play will only reduce the house edge to 3.2%.

Your post says the joker can be used for Aces, Straights, and Flushes, but the rules you linked to say the joker can be used as an Ace or to complete a Straight Flush. Which is correct? Can the joker be used to complete a regular straight or flush?